Find Amplitude, Period, and Phase Shift y=sin(3x)

Problem

y=sin(3*x)

Solution

1. Identify the standard form of the trigonometric function y=A*sin(B*(x−C))+D where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

2. Determine the value of A by looking at the coefficient of the sine function. Here, A=1

3. Calculate the amplitude using the absolute value of A

Amplitude=|1|=1

4. Determine the value of B by looking at the coefficient of x Here, B=3

5. Calculate the period using the formula (2*π)/|B|

Period=(2*π)/3

6. Determine the phase shift C Since there is no horizontal translation added or subtracted from x inside the function, C=0

Phase Shift=0

Final Answer

Amplitude=1,Period=(2*π)/3,Phase Shift=0

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